3 research outputs found
On the Edge-length Ratio of Outerplanar Graphs
International audienceWe show that any outerplanar graph admits a planar straight-line drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any Δ > 0 there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than 2 âΔ. We also show that this ratio cannot be bounded if the embeddings of the outerplanar graphs are given
On the Edge-length Ratio of Outerplanar Graphs
International audienceWe show that any outerplanar graph admits a planar straight-line drawing such that the length ratio of the longest to the shortest edges is strictly less than . This result is tight in the sense that for any there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than . We also show that every bipartite outerplanar graph has a planar straight-line drawing with edge-length ratio , and that, for any , there exists an outerplanar graph with a given combinatorial embedding such that any planar straight-line drawing has edge-length ratio greater than~